12a
0106
(K12a
0106
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 11 9 4 7 1 12 6 10
Solving Sequence
6,12
11
2,5
3 4 10 1 9 7 8
c
11
c
5
c
2
c
4
c
10
c
12
c
9
c
6
c
8
c
1
, c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
73
+ u
72
+ ··· − 2u
2
+ b, −u
43
+ 6u
41
+ ··· + a − 2, u
75
+ 2u
74
+ ··· + 2u + 1i
I
u
2
= h−2u
2
+ b + 2u + 1, a + u, u
3
− u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 78 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= hu
73
+u
72
+· · ·−2u
2
+b, −u
43
+6u
41
+· · ·+a−2, u
75
+2u
74
+· · ·+2u+1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
2
=
u
43
− 6u
41
+ ··· − 2u + 2
−u
73
− u
72
+ ··· − 3u
3
+ 2u
2
a
5
=
u
−u
3
+ u
a
3
=
−u
74
− u
73
+ ··· − 4u + 1
−u
74
− u
73
+ ··· + 3u
2
− u
a
4
=
−u
74
− u
73
+ ··· + 2u − 2
−u
74
+ u
73
+ ··· + 6u
3
− 3u
2
a
10
=
−u
2
+ 1
−u
2
a
1
=
u
4
− u
2
+ 1
u
4
a
9
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
7
=
u
13
− 2u
11
+ 5u
9
− 6u
7
+ 6u
5
− 4u
3
+ u
u
13
− u
11
+ 3u
9
− 2u
7
+ 2u
5
− u
3
+ u
a
8
=
−u
20
+ 3u
18
+ ··· − u
2
+ 1
−u
20
+ 2u
18
− 6u
16
+ 8u
14
− 11u
12
+ 10u
10
− 8u
8
+ 4u
6
− 3u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = 3u
74
+ 2u
73
+ ··· + 9u − 11
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
75
+ 42u
74
+ ··· + 39u + 1
c
2
, c
4
u
75
− 4u
74
+ ··· − u + 1
c
3
, c
7
u
75
+ u
74
+ ··· + 20u + 8
c
5
, c
11
u
75
+ 2u
74
+ ··· + 2u + 1
c
6
, c
8
u
75
− 21u
74
+ ··· − 752u + 64
c
9
, c
10
, c
12
u
75
+ 20u
74
+ ··· + 14u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
75
− 14y
74
+ ··· + 943y −1
c
2
, c
4
y
75
− 42y
74
+ ··· + 39y −1
c
3
, c
7
y
75
+ 21y
74
+ ··· − 752y −64
c
5
, c
11
y
75
− 20y
74
+ ··· + 14y −1
c
6
, c
8
y
75
+ 61y
74
+ ··· + 232704y −4096
c
9
, c
10
, c
12
y
75
+ 72y
74
+ ··· − 10y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.887145 + 0.421919I
a = −1.304670 + 0.309765I
b = −1.36625 + 1.06588I
0.04333 − 6.34447I −7.93297 + 10.47635I
u = 0.887145 − 0.421919I
a = −1.304670 − 0.309765I
b = −1.36625 − 1.06588I
0.04333 + 6.34447I −7.93297 − 10.47635I
u = −0.990634 + 0.243871I
a = 0.370425 − 0.564934I
b = 0.509716 − 0.608237I
−4.44660 + 0.09147I −11.59766 + 0.I
u = −0.990634 − 0.243871I
a = 0.370425 + 0.564934I
b = 0.509716 + 0.608237I
−4.44660 − 0.09147I −11.59766 + 0.I
u = 1.000630 + 0.265543I
a = 2.03967 + 0.36176I
b = 1.38837 − 1.74230I
−8.14996 − 1.57539I −15.1216 + 0.I
u = 1.000630 − 0.265543I
a = 2.03967 − 0.36176I
b = 1.38837 + 1.74230I
−8.14996 + 1.57539I −15.1216 + 0.I
u = −1.002040 + 0.280364I
a = −2.56830 − 0.43571I
b = −1.18117 − 1.37862I
−8.06174 + 4.47030I 0
u = −1.002040 − 0.280364I
a = −2.56830 + 0.43571I
b = −1.18117 + 1.37862I
−8.06174 − 4.47030I 0
u = 0.997744 + 0.300446I
a = 0.162900 + 0.569242I
b = 0.500726 + 0.752913I
−4.11035 − 5.87109I 0
u = 0.997744 − 0.300446I
a = 0.162900 − 0.569242I
b = 0.500726 − 0.752913I
−4.11035 + 5.87109I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.023860 + 0.232154I
a = 2.01282 − 0.17234I
b = 1.11389 + 1.64325I
−7.89110 − 4.43076I 0
u = −1.023860 − 0.232154I
a = 2.01282 + 0.17234I
b = 1.11389 − 1.64325I
−7.89110 + 4.43076I 0
u = −0.930948 + 0.071026I
a = 1.266100 + 0.027107I
b = 1.047670 + 0.599871I
−1.97213 − 1.46805I −10.98188 + 4.43556I
u = −0.930948 − 0.071026I
a = 1.266100 − 0.027107I
b = 1.047670 − 0.599871I
−1.97213 + 1.46805I −10.98188 − 4.43556I
u = 1.023180 + 0.307631I
a = −2.48345 + 0.20439I
b = −1.21466 + 1.45040I
−7.44212 − 10.73660I 0
u = 1.023180 − 0.307631I
a = −2.48345 − 0.20439I
b = −1.21466 − 1.45040I
−7.44212 + 10.73660I 0
u = 0.745430 + 0.809040I
a = −0.366987 − 1.071930I
b = −2.70214 − 0.22546I
−1.06539 − 5.24431I 0
u = 0.745430 − 0.809040I
a = −0.366987 + 1.071930I
b = −2.70214 + 0.22546I
−1.06539 + 5.24431I 0
u = 0.882590 + 0.702538I
a = −0.829874 − 0.592338I
b = −1.79400 + 1.05298I
2.08360 − 2.69427I 0
u = 0.882590 − 0.702538I
a = −0.829874 + 0.592338I
b = −1.79400 − 1.05298I
2.08360 + 2.69427I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.743473 + 0.453790I
a = 0.007570 − 0.366607I
b = −0.316775 + 0.512887I
1.49999 − 2.25964I −3.17178 + 5.04191I
u = 0.743473 − 0.453790I
a = 0.007570 + 0.366607I
b = −0.316775 − 0.512887I
1.49999 + 2.25964I −3.17178 − 5.04191I
u = 0.795943 + 0.812291I
a = −0.495301 − 0.730597I
b = −0.970310 + 0.264145I
2.31304 − 1.29591I 0
u = 0.795943 − 0.812291I
a = −0.495301 + 0.730597I
b = −0.970310 − 0.264145I
2.31304 + 1.29591I 0
u = −0.786206 + 0.833290I
a = −0.548362 + 1.180140I
b = −3.10995 − 0.03398I
−1.046790 − 0.233605I 0
u = −0.786206 − 0.833290I
a = −0.548362 − 1.180140I
b = −3.10995 + 0.03398I
−1.046790 + 0.233605I 0
u = 0.788338 + 0.844997I
a = −0.39372 + 2.64094I
b = 3.47934 + 2.39014I
−0.77118 + 3.07466I 0
u = 0.788338 − 0.844997I
a = −0.39372 − 2.64094I
b = 3.47934 − 2.39014I
−0.77118 − 3.07466I 0
u = −0.795768 + 0.856610I
a = −0.458519 + 0.581639I
b = −0.661200 − 0.385202I
3.38785 − 4.33505I 0
u = −0.795768 − 0.856610I
a = −0.458519 − 0.581639I
b = −0.661200 + 0.385202I
3.38785 + 4.33505I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.784804 + 0.867935I
a = −0.16460 − 2.47990I
b = 3.54552 − 1.97189I
0.25516 − 9.43024I 0
u = −0.784804 − 0.867935I
a = −0.16460 + 2.47990I
b = 3.54552 + 1.97189I
0.25516 + 9.43024I 0
u = −0.761209 + 0.303390I
a = −0.66189 − 1.48897I
b = −0.843213 − 1.134480I
−2.11424 + 2.43489I −12.3251 − 6.9587I
u = −0.761209 − 0.303390I
a = −0.66189 + 1.48897I
b = −0.843213 + 1.134480I
−2.11424 − 2.43489I −12.3251 + 6.9587I
u = 0.875605 + 0.815188I
a = −1.64111 + 0.93843I
b = 0.07441 + 2.48036I
4.23581 − 1.11329I 0
u = 0.875605 − 0.815188I
a = −1.64111 − 0.93843I
b = 0.07441 − 2.48036I
4.23581 + 1.11329I 0
u = −0.891540 + 0.799179I
a = −1.006990 + 0.953772I
b = −2.96795 − 1.32514I
2.74184 + 2.99741I 0
u = −0.891540 − 0.799179I
a = −1.006990 − 0.953772I
b = −2.96795 + 1.32514I
2.74184 − 2.99741I 0
u = −0.858105 + 0.855314I
a = −0.72834 − 1.53155I
b = 1.71110 − 1.68955I
7.80149 − 3.18910I 0
u = −0.858105 − 0.855314I
a = −0.72834 + 1.53155I
b = 1.71110 + 1.68955I
7.80149 + 3.18910I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.911589 + 0.805325I
a = 0.91456 − 1.70167I
b = −1.01479 − 2.88671I
4.12505 − 4.94897I 0
u = 0.911589 − 0.805325I
a = 0.91456 + 1.70167I
b = −1.01479 + 2.88671I
4.12505 + 4.94897I 0
u = −0.880512 + 0.845442I
a = 0.187760 + 0.773523I
b = −0.238660 + 0.915735I
8.84457 + 1.81738I 0
u = −0.880512 − 0.845442I
a = 0.187760 − 0.773523I
b = −0.238660 − 0.915735I
8.84457 − 1.81738I 0
u = 0.965168 + 0.770733I
a = −0.697279 − 0.434511I
b = −1.42752 + 0.24371I
1.79639 − 4.64940I 0
u = 0.965168 − 0.770733I
a = −0.697279 + 0.434511I
b = −1.42752 − 0.24371I
1.79639 + 4.64940I 0
u = 0.982212 + 0.751243I
a = −1.32097 − 0.56552I
b = −2.17734 + 2.46253I
−1.77467 − 0.61424I 0
u = 0.982212 − 0.751243I
a = −1.32097 + 0.56552I
b = −2.17734 − 2.46253I
−1.77467 + 0.61424I 0
u = −0.923652 + 0.829415I
a = −0.726145 − 0.285385I
b = −0.224702 − 0.630733I
8.70938 + 4.41281I 0
u = −0.923652 − 0.829415I
a = −0.726145 + 0.285385I
b = −0.224702 + 0.630733I
8.70938 − 4.41281I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.730137 + 0.191745I
a = 0.848146 + 0.745655I
b = 2.01940 − 0.38270I
−2.75312 − 0.71407I −10.56661 + 9.33379I
u = 0.730137 − 0.191745I
a = 0.848146 − 0.745655I
b = 2.01940 + 0.38270I
−2.75312 + 0.71407I −10.56661 − 9.33379I
u = −0.976675 + 0.776780I
a = −1.35830 + 0.69537I
b = −2.55017 − 2.46709I
−1.63091 + 6.25511I 0
u = −0.976675 − 0.776780I
a = −1.35830 − 0.69537I
b = −2.55017 + 2.46709I
−1.63091 − 6.25511I 0
u = −0.944507 + 0.823662I
a = 1.48146 + 0.76707I
b = 0.86627 + 3.04060I
7.53164 + 9.43047I 0
u = −0.944507 − 0.823662I
a = 1.48146 − 0.76707I
b = 0.86627 − 3.04060I
7.53164 − 9.43047I 0
u = 0.980512 + 0.782944I
a = 2.68521 − 0.41044I
b = 2.09440 − 4.67862I
−1.36386 − 9.14996I 0
u = 0.980512 − 0.782944I
a = 2.68521 + 0.41044I
b = 2.09440 + 4.67862I
−1.36386 + 9.14996I 0
u = −0.982139 + 0.791682I
a = −0.527120 + 0.395419I
b = −1.306180 + 0.059161I
2.80938 + 10.47360I 0
u = −0.982139 − 0.791682I
a = −0.527120 − 0.395419I
b = −1.306180 − 0.059161I
2.80938 − 10.47360I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.992674 + 0.791962I
a = 2.52753 + 0.15259I
b = 2.39427 + 4.34125I
−0.3915 + 15.6011I 0
u = −0.992674 − 0.791962I
a = 2.52753 − 0.15259I
b = 2.39427 − 4.34125I
−0.3915 − 15.6011I 0
u = 0.473511 + 0.518700I
a = 0.569905 − 0.044011I
b = −0.573438 − 0.122440I
2.29195 − 1.37822I −0.58151 + 4.13567I
u = 0.473511 − 0.518700I
a = 0.569905 + 0.044011I
b = −0.573438 + 0.122440I
2.29195 + 1.37822I −0.58151 − 4.13567I
u = 0.067050 + 0.682615I
a = −0.17440 − 2.58690I
b = 0.05480 − 1.96512I
−4.40078 + 7.33498I −7.71783 − 5.68958I
u = 0.067050 − 0.682615I
a = −0.17440 + 2.58690I
b = 0.05480 + 1.96512I
−4.40078 − 7.33498I −7.71783 + 5.68958I
u = −0.643142
a = 0.787276
b = 0.179262
−0.881194 −11.4850
u = 0.311673 + 0.555828I
a = 0.20614 − 1.83508I
b = −0.354502 − 0.754446I
1.74635 + 2.74612I −2.00357 − 4.26795I
u = 0.311673 − 0.555828I
a = 0.20614 + 1.83508I
b = −0.354502 + 0.754446I
1.74635 − 2.74612I −2.00357 + 4.26795I
u = −0.016299 + 0.632498I
a = −0.07873 + 2.68758I
b = 0.42918 + 1.85147I
−5.01681 − 1.39047I −8.94216 + 0.64791I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.016299 − 0.632498I
a = −0.07873 − 2.68758I
b = 0.42918 − 1.85147I
−5.01681 + 1.39047I −8.94216 − 0.64791I
u = 0.064333 + 0.625670I
a = 1.135470 − 0.066066I
b = 0.327673 − 0.145405I
−1.22393 + 2.66490I −4.46846 − 2.68862I
u = 0.064333 − 0.625670I
a = 1.135470 + 0.066066I
b = 0.327673 + 0.145405I
−1.22393 − 2.66490I −4.46846 + 2.68862I
u = −0.363118 + 0.189476I
a = 2.22576 + 0.86434I
b = 0.348541 + 0.046158I
−1.083860 − 0.035362I −8.47943 − 1.04313I
u = −0.363118 − 0.189476I
a = 2.22576 − 0.86434I
b = 0.348541 − 0.046158I
−1.083860 + 0.035362I −8.47943 + 1.04313I
12
II. I
u
2
= h−2u
2
+ b + 2u + 1, a + u, u
3
− u
2
+ 1i
(i) Arc colorings
a
6
=
0
u
a
12
=
1
0
a
11
=
1
−u
2
a
2
=
−u
2u
2
− 2u − 1
a
5
=
u
−u
2
+ u + 1
a
3
=
0
u
2
− u
a
4
=
0
u
2
− u
a
10
=
−u
2
+ 1
−u
2
a
1
=
−u
u
2
− u − 1
a
9
=
0
u
a
7
=
0
u
a
8
=
0
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 2u
2
+ u − 14
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
6
, c
7
c
8
u
3
c
4
(u + 1)
3
c
5
u
3
+ u
2
− 1
c
9
, c
10
u
3
− u
2
+ 2u − 1
c
11
u
3
− u
2
+ 1
c
12
u
3
+ u
2
+ 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
6
, c
7
c
8
y
3
c
5
, c
11
y
3
− y
2
+ 2y −1
c
9
, c
10
, c
12
y
3
+ 3y
2
+ 2y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.877439 − 0.744862I
b = −2.32472 + 1.12456I
1.37919 − 2.82812I −12.69240 + 3.35914I
u = 0.877439 − 0.744862I
a = −0.877439 + 0.744862I
b = −2.32472 − 1.12456I
1.37919 + 2.82812I −12.69240 − 3.35914I
u = −0.754878
a = 0.754878
b = 1.64944
−2.75839 −13.6150
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
75
+ 42u
74
+ ··· + 39u + 1)
c
2
((u − 1)
3
)(u
75
− 4u
74
+ ··· − u + 1)
c
3
, c
7
u
3
(u
75
+ u
74
+ ··· + 20u + 8)
c
4
((u + 1)
3
)(u
75
− 4u
74
+ ··· − u + 1)
c
5
(u
3
+ u
2
− 1)(u
75
+ 2u
74
+ ··· + 2u + 1)
c
6
, c
8
u
3
(u
75
− 21u
74
+ ··· − 752u + 64)
c
9
, c
10
(u
3
− u
2
+ 2u − 1)(u
75
+ 20u
74
+ ··· + 14u + 1)
c
11
(u
3
− u
2
+ 1)(u
75
+ 2u
74
+ ··· + 2u + 1)
c
12
(u
3
+ u
2
+ 2u + 1)(u
75
+ 20u
74
+ ··· + 14u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
3
)(y
75
− 14y
74
+ ··· + 943y −1)
c
2
, c
4
((y −1)
3
)(y
75
− 42y
74
+ ··· + 39y −1)
c
3
, c
7
y
3
(y
75
+ 21y
74
+ ··· − 752y −64)
c
5
, c
11
(y
3
− y
2
+ 2y −1)(y
75
− 20y
74
+ ··· + 14y −1)
c
6
, c
8
y
3
(y
75
+ 61y
74
+ ··· + 232704y −4096)
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)(y
75
+ 72y
74
+ ··· − 10y −1)
18
